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Evaluate F. dS, S where F(x, y, z) = (3xz – Vy? + 2?, sin(x – 2), e" - z²) and S is the surface which is the boundary of the region between the sphere x2 + y² + z² = 4 and the cone x² + y? = z² above the xy-plane, oriented outward. See the figure to the right. (Note: while it looks like there's a hole in the top of the object, that is just a rendering artifact - there is no hole there.)

Evaluate F. dS, S where F(x, y, z) = (3xz – Vy? + 2?, sin(x – 2), e" - z²) and S is the surface which is the boundary of the region between the sphere x2 + y² + z² = 4 and the cone x² + y? = z² above the xy-plane, oriented outward. See the figure to the right. (Note: while it looks like there's a hole in the top of the object, that is just a rendering artifact - there is no hole there.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Evaluate F. dS, S where F(x, y, z) = (3xz – Vy? + 2?, sin(x – 2), e" – z²) and S is the surface which is the boundary of the region between the sphere x2 + y² + z² = 4 and the cone x² + y? = z² above the xy-plane, oriented outward. See the figure to the right. (Note: while it looks like there's a hole in the top of the object, that is just a rendering artifact - there is no hole there.)
Transcribed Image Text:Evaluate F. dS, S where F(x, y, z) = (3xz – Vy? + 2?, sin(x – 2), e" – z²) and S is the surface which is the boundary of the region between the sphere x2 + y² + z² = 4 and the cone x² + y? = z² above the xy-plane, oriented outward. See the figure to the right. (Note: while it looks like there's a hole in the top of the object, that is just a rendering artifact - there is no hole there.)
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